2014-03-16
Material and Methods
Extensive data screening was performed to check for anomalous/erroneous data values.
(a) Cross tabulations to ensure that a consistent names was used for all sites over all years in the
study and they sites were assigned to the appropriate basin. [Pages 1-3]
(b) Transect information from October, November and December was removed so that all data in a
year comes from the January -> May window. [Pages 4-6]. Most sites were measured only in
March and April, but some sites (usually in earlier years) were also measured in
January/February.
(c) The total number of measurements was examined for each site-year combination. [Pages 7-15]
Cases where the number of measurements were not a multiple of 10 were investigated. [Pages
17-23] At the same time, it was verified that missing data represented measurements not taken,
and that a measurement of 0 represented a measurement taken, but no snow was present. The
former was removed from the analyses; the latter were retained in subsequent analyses.
(d) Plots of the mean snow depth vs the mean snow depth over the measurements on a transect
[page 24] were used to identify site-year combinations where the summary statistics were more
than 30% different [pages 25-27]. These site-year combinations were investigated further to
ensure that no anomalous values were present on a transect. Similarly, transects where the
standard deviation of the depth measurements were unusually large were also reviewed. [Pages
28-38] A similar screening was performed for SWE [pages 38- 52] and for Density [pages 53-56].
Any errors in the raw data were corrected.
(e) A comparison of the time when the maximum depth, SWE, and density occurred showed that
the yearly maximum always occurred on the same transect [page 66]
(f) Plots of the mean depth, mean SWE, mean density, maximum depth, maximum SWE, and
maximum density over transects in a year) vs time were used to identify sites within each basin
whose values appeared to be anomalous [pages 71-100]
Following data screening, the data was reduced by finding the average snow depth, SWE, and density
for each transect.
Changes in yearly maximum average snow depth/ average SWE/ average Density over time.
The yearly maximum average snow depth/ average SWE/ average Density was determined in each
calendar year (in January-May) for each site across any multiple transects during this period. A mixedlinear model was fit to each basin using SAS Proc Mixed. The model in standard notation is:
Y = Year + Site(R) +AR(1)
where Y represents the variable of interest (max average depth, max average SWE, or max average
density); Year represents the year effect and the coefficient estimates the common trend (slope);
Site(R) represent the random effect of each Site within each basin; and AR(1) represents autoregressive
(lag 1) model for the residuals.. This model give a series of parallel lines (one for each site within a basin)
all with the common slope. The autoregressive form of the residuals allows for serial correlation among
the residual over time that allow for external, long-term effects where the residuals could be
simultaneously affected for several years in a row.
A model with separate slopes for each site was also fit to examine if the trend was common to all sites
within the basin.
Changes in seasonal maximum average snow depth.SWE/Density over time.
The maximum average snow depth/average SWE/ average density was determined for four “seasons”
in each year – early and late March and early and late April for each site. Data from outside the
March/April period was excluded. This portioning may lead to basins where not all seasons have
sufficient data as shown on page 132.[You likely want at least 20+ observations in each basin-season
combination – have a look at the plots on page 133-189 to see the cases with rich and poor data as well.
A mixed-linear model was fit to each basin to determine if the trend was common across the four
seasons using SAS Proc Mixed. The model in standard notation is:
Y = Year + Season + Year*Season Site(R) +AR(1)
where Y represents the variable of interest (max depth, max SWE, or max density); Year represents the
year effect and the coefficient estimates the common trend (slope); Season represents the effect of
season (i.e. an upwards or downward impact of the season); Year*Season represents the differential
slopes across the seasons; Site(R) represent the random effect of each Site within each basin; and AR(1)
represents autoregressive (lag 1) model for the residuals.. This model give a series of parallel lines (one
for each site within a basin) all with the common slope. The autoregressive form of the residuals allows
for serial correlation among the residual over time that allow for external, long-term effects where the
residuals could be simultaneously affected for several years in a row. A model with separate slopes for
each site was also fit, but did not provide an improvement over the above model.
Meterological variables – yearly trends
Daily meterological data was available for two stations – Yellowknife Airport and Hay River airport. Long
term trends were examined for total (calendar) yearly rainfall, snow fall, total precipitation,and
maximum snow on the ground. The total snow to total precipitation ratio was also computed. The
length of the snow season (defined as the first date with snow-on-the ground to the last date with
snow-on-the ground was also computed from the fall of the previous year to June of the current year.
A mixed-linear model was fit for each of these six variables in each basin using SAS Proc Mixed. The
model in standard notation is:
Y = Year +AR(1)
where Y represents the variable of interest (e.g. total yearly rainfall); Year represents the year effect and
the coefficient estimates the trend (slope); and AR(1) represents autoregressive (lag 1) model for the
residuals. The autoregressive form of the residuals allows for serial correlation among the residual over
time that allow for external, long-term effects where the residuals could be simultaneously affected for
several years in a row.
Predicting maximum snow depth from met stations.
The date at which maximum average snow depth occurred was matched with the meteorological data
for that same date for sites in Basin 1 and Basin 6. Sites in Basin 2 were matched to the meteorological
data from Hay River; sites in Basin 3 were matched to the meteorological data from Yellowknife Airport.
A regression model was fit for each site (in standard notation)
MaxAverageDepth = SnowOnGround + AR(1)
Where MaxAverageDepth is the maximum average depth of snow at each site in each year;
SnowOnGround is the measured snow on ground at the match meteorological station on the date when
the maximum average depth of snow occurred at that site in that year; and AR(1) is the autoregressive
error structure for the residuals as used in the previous models.
Results:
Page 16 – A plot of when each site was sampled showed that the majority of sites were sampled
between 1980 and the present with only a few sites sampled prior to 1980. Sampling frequency has
declined after 2000 with many sites having reduced sampling effort.
Page 102. .
There was no evidence of a differential trend across the sites within a basin (results not shown) which is
not surprising given the large amount of variability within each site over time.
There was evidence of an increase in maximum snow depth and maximum SWE (but not maximum
density) over time for basin 2 (respectively, and evidence of a decline in same variables for basin 6. In
basin 3, there was evidence of a increase in max SSW and Density (but not maximum depth). Plots of the
overall trend are shown on Pages 103-117
Page 192. There was no evidence that the trend line varied by season for any variable except for max
average SWE and max average depth in basins 2 and 6. However, this may be an artefact of the
sampling process as no data was available prior to 1990 on all the season and there is evidence from the
plot of a change point around 1990. Plots of the seasonal trends are found on Pages 193-202
Page 214 No evidence of a trend in the meteorological variables was found except at Hay River for an
increasing trend in total rainfall, and an increasing trend at Yellowknife Airport for total snowfall. Plots
of the fitted trend lines are found on page 215 – 226
Pages 231-234 show the relationship of the Maximum Snow Depth at each site/year vs. the
corresponding snow on ground at the matched meteorological station. Page 235-236 There was
evidence that the snow on ground at the matched meteorological station station had predictive ability
for the maximum average snow depth for 4/7 sites in Basin 1, for 9/10 sites In Basin 2, for 1 of 10 sites in
Basin 3, and for 8/9 sites in Basin 6. Generally, the airports had predictive ability for sites In the same
basin, but were not good predictors for out-of-basin sites. However, as seed by the Pages 237-276, the
variance around the predicted line is very large and so is unlikely to be useful in predicting for specific
years.